Mean curvature: Difference between revisions
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The '''mean curvature''' of a [[Riemannian manifold]] at a point on the Riemannian manifold is defined as the trace of the [[shape operator]] at that point. In other words, the mean curvature is a function that associates to every point the trace of the shape operator at the point. | The '''mean curvature''' of a [[Riemannian manifold]] at a point on the Riemannian manifold is defined as the trace of the [[shape operator]] at that point. In other words, the mean curvature is a function that associates to every point the trace of the shape operator at the point. | ||
The mean curvature function is denoted as <math>H</math>. | |||
==Related notions== | ==Related notions== | ||
Latest revision as of 19:48, 18 May 2008
This article defines a notion of curvature for a differential manifold equipped with a Riemannian metric
This article defines a scalar function on a manifold, viz a function from the manifold to real numbers. The scalar function may be intrinsic or defined in terms of some other structure/functions
Definition
In terms of the shape operator
The mean curvature of a Riemannian manifold at a point on the Riemannian manifold is defined as the trace of the shape operator at that point. In other words, the mean curvature is a function that associates to every point the trace of the shape operator at the point.
The mean curvature function is denoted as .